Fibonacci Identities and Graph Colorings
Abstract
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as \[F_{r+s+t} = F_{r+1}F_{s+1}F_{t+1} + F_r F_s F_t - F_{r-1}F_{s-1}F_{t-1}.\]
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2008
- DOI:
- 10.48550/arXiv.0805.0992
- arXiv:
- arXiv:0805.0992
- Bibcode:
- 2008arXiv0805.0992H
- Keywords:
-
- Mathematics - Combinatorics;
- Mathematics - General Mathematics;
- 05C15;
- 05A19;
- 05C38
- E-Print:
- 5 pages, 1 figure